ECM104 Quantitative Research Methods

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ECM104 Quantitative Research Methods
Assessed Exercise 2020-2021
The Dynamic Relationship Between Unemployment in London and Other
Regions of the United Kingdom
This exercise is used to evaluate the ECM104 module. It counts for 100% of the mark for the
module. There are no other exercises and no examination.
You must use Stata to complete the work. Do not use directly copied and pasted results tables from
Stata in the main text of your answers. Any Stata output you wish to present should appear in
clearly labelled appendices placed at the end of your write-up. These should be appropriately
referenced in the main part of your solutions so material you refer to is easy to locate. In your main
text present only the key results required in as succinct a way as possible. Certainly do not provide
additional output that does not address the question.1
Warning
This work must be conducted on an individual basis. It is expected and required that each
person’s work should be clearly their own and not be identical to any part of any other
person’s work, including that of other students.
Deadline for Completion of this Assessed Exercise
The deadline for the submission of this assignment is
12.00 noon Friday January 22nd 2021
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You must summarize the results from Stata in your answers. The complete output tables may include a lot of
information that is not needed for the answer, in which case it should not appear. The complete tables should appear in
an appendix to show that you have used Stata to complete the exercise.
Department of
Economics
University of Reading
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Introduction
Unemployment, and the impact of economic crises, tend to vary across space as well as time. It is
therefore of interest to explore how the unemployment rates of different regions are related. In
particular, concerning the UK, London and the south-east of England display persistently lower
unemployment rates than other regions of the country. In this exercise you will explore the
relationship between the unemployment rate in London and another UK region.
You will apply the time series techniques considered in ECM104 lectures and classes, including
unit root tests, diagnostic testing of models, cointegration analysis, and error correction modelling.
Koop (2013) discusses these methods (see especially chapters 9, 10, and 11). 2
Data
The data is contained in the Excel file called ‘Regional Unemployment Data (2020) (2)’ available in
the Assignments section of the Blackboard site. It contains monthly data for London and eleven
other UK regions. These are given in table 1 below.
Table 1: Regions and Variable Names

The data also includes a variable Date which provides the year and month of each observation.
The data are in percentage terms, and seasonally adjusted, for the period April 1992 to July 2020
inclusive (340 observations). The last few observations coincide with the onset of the COVID-19
pandemic. The data were obtained from the website of the UK Office for National Statistics (Office
for National Statistics, 2020).
For this question, you are required to consider two series, that for London and one for another UK
region. The other regional series you must use is determined by the allocation rule given in table 2
below.
Import the data into Stata and identify the series you will use. Set up a monthly time variable based
on the variable Date. Use the gen and tsset commands introduced in Stata Exercise 5.3
2 Useful texts including sections on unit root testing and cointegration are Brooks (2003) and Patterson (2000).
3 The commends required are:
gen Month=monthly(Date, “YM”)
tsset Month, monthly
3
Table 2: Series by Student Number

Questions
1. Ocular Econometrics
a) Provide time series line plots of each of your two unemployment series. (10 marks)
b) Describe the evolution of the series over time commenting especially on any co-movements or
changes in behaviour over time and the stationarity or otherwise of the series. (10 marks)
2. Non-Stationarity of Unemployment
Use augmented Dickey-Fuller (ADF) tests with an intercept to determine the order of integration of
your two series. Recall that you will have to select an appropriate augmentation order for the tests.
This is best done using an information criterion. (8 marks)
3. The Long Run Relationship Between Unemployment in London and the Other Region
a) Determine if your two unemployment series are cointegrated using the Engle-Granger procedure.
(See Stata Exercise 5 for how to do this). Use London as the explanatory variable, not the
dependent variable. (8 marks)
b) Comment on the value of the slope coefficient in the cointegrating regression. (8 marks)
c) Save the residuals from the cointegrating regression as RES1 and provide a time series plot of
them. Comment any particular characteristics you observe in the graph. (8 marks)
4. The Dynamic Relationship Between Unemployment Rates: Error Correction Models
a) Estimate two error correction models for the relationship between your unemployment series.
One should have no additional lags of the differences (equation (1)), the other should include 8 lags
of the differences (model (2)).4 Let L represent the unemployment rate in London and OTHER that
4 Remember and error correction model uses the differences of the variables of interest and the lagged residuals from
the cointegrating regression.
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of your other region. Then the models you should estimate are set out in equations (1) and (2):
t o t t t
 OTHER    L  RES  u
  1  2 1 1 , (1)
t
i
i t
i
t o t t i t
 OTHER    L  RES    L    OTHER  u



 
8
1
1
8
1
  1  2 1 1  1 

where OTHER is the unemployment rate of your other region,  is the differencing operator such
that
 X t  X t  X t  1 , u t is the regression disturbance, and  i , i  0 ,1,2  i , i  1,2 ,…, 8 , and
, i  1,2 ,…, 8
i
 are coefficients.5 (8 marks)
b) Use diagnostic tests6 of the model errors and information criteria to determine which of these
models is superior. (8 marks)
c) Use your preferred model to consider the following.
i) How, in the long run, does unemployment in your other region adjust to that in London?
Is the adjustment significant? (8 marks)
ii) How statistically reliable is the model on which you base these conclusions? (8 marks)
iii) Does your estimated equation include any insignificant coefficients? (8 marks)
iv) What impact, if any, has the COVID-19 pandemic had on your results. Explain.
(8 marks)
References
Brooks, C. (2002) Introductory Econometrics for Finance. Cambridge. Cambridge
University Press.
Koop. G. (2013) Analysis of Economics Data (fourth edition). Chichester: Wiley
Office for National Statistics (2020)
https://www.ons.gov.uk/employmentandlabourmarket/peopleinwork/employmentandemploy
eetypes/datasets/labourmarketstatistics Accessed 5/11/2020.
Patterson, K.D. (2000) An Introduction to Applied Econometrics: a Time Series Approach.
New York: St. Martin’s Press.
Simon P. Burke
November 5th 2020
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Note that in equations (1) and (2), terms in L appear on the right hand side only. This is consistent with the long run
relationship estimated in question 3, part a), which must have L on the right hand side as well (i.e. as the explanatory
variable).
6 Diagnostic tests are the tests of serial correlation, heteroscedasticity and non-normality of the model errors.